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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23080 |
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Table of Contents:
- For all $s\in[0,1]$ and $t\in(0,s]\cup [2-s,2)$, we find the supremum of numbers $ω\in(0,2)$ such that $\text{I}_ω(μ\astσ) \lesssim 1$, where $μ$ is any Borel measure on $B(1)$ with $\text{I}_t(μ)\leq 1$ and $σ$ is any $(s,1)$-Frostman measure on a $C^2$-graph with non-zero curvature. As an application, we use this to show the sharp $L^6$-decay of Fourier transform of $σ$ when $s\in [\frac{2}{3}, 1]$.